Cause and effect is one way of looking at things: the reason that x happened is that y caused x
Choice and intentionality is a different way of looking at things: the reason that I did X is that on the basis of Y and because of the absence of z and so forth I chose to do X (and nothing got in my way and stopped me from doing so).
I only place free will in opposition to absolute determinism, and what I mean by absolute determinism is the position that “because it is true that y caused x, it is bullshit that you chose to do x and that x happened because you chose it; that’s an illusion, the truth is determinism”.
Warning: analogy ahead
When asked what this little bonsai tree on my desk really is, I can answer that it is an organism and give genus and species; or I can state that it is a complex of chemical interactions; or that it is a set of the following atoms each of which has a physical location and a relationship of connectivity and interaction with the atoms surrounding it; or that it is a composite of interactions between subatomic particles with energy levels and behaviors as specified thusly, etc etc. None of those explanations is false. Hence the truth of any given one of them does not negate the truth of any of the others. Any appearance that they are mutually contradictory is an illusory appearance.
/corny analogy
I don’t consider myself to possess free will in a sense that yonder kitty cat does not. I’m not even disposed to say that I possess free will in a sense that the bonsai tree does not. If there are pervasive illusions that I don’t think we’ve finished unravelling, the central one may be “who is the self”. I strongly suspect it resides in interactivity rather than existing in individual bodies, but whatever the self actually is, it is conscious and it does things on purpose and not as a result of something else causing it. That’s what I mean by free will. I can’t say whether what other folks mean when they speak of free will is entirely compatible; I don’t respect their right to patent the phrase and it’s a plain English phrase and I’m allowed to interpret it as such.